I need help with this problem it says to find the area of each shaded sector and round to the hundredth place

The result from using Option 2 will be significantly less than the result from using Option 1 over a period of 20 years.

Given,

Belinda wants to invest $1,000.

The Table is:
Number of years 1 2 3

Option 1 (amount in dollars) 1100 1200 1300

Option 2 (amount in dollars) 1100 1210 1331

Now, According to the question:

When the x-values are sequential (1, 2, 3, ...), the y-values will have a common difference for a linear function, and a common ratio for an exponential function.

For the two investment options, we notice Belinda earns 1300 -1000 = 300 the first year for either option. The difference is the same the next year for Option 2 (1600 -1300 = 300), but is not the same for Option 1. For that option, the ratio is the same for the second year as it was for the first year:

1690/1300 = 1.3 = 1300/1000

Part A :
(Option 1) can be represented by exponential function.

(Option 2) can be represented by a linear function.

Part B:

For Option 1:

To find the value of the investment f(n), in dollars, after n years.

The generic form of an exponential function is ...

f(n) = a·b^n

Now, Amount after 1 year = 1100

Principle (P) is = 1000

Using the formula :

A = P[tex](1+r)^n[/tex]

1100 = 1000[tex]([/tex][tex]1 + r)^1[/tex]

1.10 = 1 + r

r = 0.10

Amount after t years can be given by :

A = 1000(1.10)^t

For Option 2,

The generic form of an exponential function is ...

f(n) = a·n + b

Rate of change (m) = (1100 - 1000) / 1 = 100

Amount after t years can be given by

A = 1000 + 100 x t .

Part C:

Investment in (1) : 1000 [tex](1.10)^2^0[/tex]= $6727

Investment in (2): $3000

Hence, The result from using Option 2 will be significantly less than the result from using Option 1 over a period of 20 years.

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The value of the unknown angle is as follows;

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.

Therefore, the angle 4 can be found as follows:

∠4 = 8x + 6 (alternate angles)

Hence,

8x + 6 + 118 = 180(sum of angles on a straight line)

8x = 180 - 118 - 6

8x = 56

divide both sides by 8

x = 56 / 8

x = 7

Therefore,

∠4 = 8(7) + 6 = 56 + 6 = 62 degrees

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Answer:

Step-by-step explanation:

first row: 4

second: 2

third: 6

fourth: 9

plug in x for x in the equation/plug in y for y in the equation for whichever is given.

Answer:

Combine [tex]\frac{3}{2 }[/tex] and | x - 2 |

[tex]y\frac{3|x-2|}{2}[/tex]

By using the fact that the interior angles of a triangle must add up to 180, we will see that the value of x is 15.

Here we have 3 expressions for the measures of the interior angles of a triangle.

Now, remember that the sum of the interior angles of a triangle is always equal to 180°, then we can write:

(8x - 7)° + (x + 7)° + (2x + 15)° = 180°

Ignoring the degrees and solving this for x, we get:

8x - 7 + x + 7 + 2x + 15 = 180

11x + 15 = 180

11x = 180 - 15 = 165

x = 165/11  =15

The value of x is 15.

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SOLUTION

Given:

Final answer:

-2.7121

To find the x intercept of the equation make y=0 and solve for x.

The x intercept is 3/2

To find the y intercept, make x=0 and solve for y

The y intercept is 12.

Answer:

48°

Explanation:

A line always equals 180°. The angle on the right is a 90° angle (we know this because or the little red box shown) and the angle in the middle is 42°. We would add 42° and 90° to get the combination of both which is 132°

42+90=132

Then subtract 132° from 180° to find unknown angle b.

180-132=48

Unknown angle b= 48°

Answer: 20, 10

Step-by-step explanation:

Let the width be w. Then, the length is 2w. Substituting into the formula for the perimeter of a rectangle,

[tex]2(w+2w)=60\\\\w+2w=30\\\\3w=30\\\\w=10\\\\\implies 2w=2(10)=20[/tex]

In order to graph this equation, we need at least two points that are solution to the equation.

To find these points, we can choose values for x and then calculate the corresponding values of y.

Choosing the x-values of -2, -1, 0 and 1, we have:

So we have the points (-2, 4), (-1, 1.5), (0, -1) and (1, -3.5). Graphing these points and the line that passes through them, we have:

The expression for M in terms of other variables is M = Fr^2/Gm

The variable being calculated is the formula's subject. On one side of the equals sign, it is identifiable as the letter on its own.

In order to make one of the the variables the subject of the formula, we place rewrite the expression in a different form.

Given the formula to calculate the gravitational force between two objects as;

Fg = GMm/r^2

We are to make M the subject of the formula in terms of other variables.

F = GMm/r^2

Cross multiply

Fr^2 = GMm

Divide both sides by Gm

Fr^2/Gm = GMm/Gm

Fr^2/Gm = M

Swap

M = Fr^2/Gm

This gives the expression for the variable M.

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The x-intercept is where the graph passes the x-axis.

The graph extends from {-5 ≤ x ≤ 3}

The x-intercept is {x = -1}.

we know that

the formula to calculate teh slope between two points is equal to

where

(x1,y1) is one point

and

(x2,y2) is the other point

substitute the values in the formula and solve for m

Example

you have the points

(1,4) and (3,2)

so

(x1,y1)=(1,4)

(x2,y2)=(3,2)

substitute in te formula

m=(2-4)/(3-1)

m=-2/2

m=-1

the slope is -1

The answer is not correct. There is a mistake applying the distributive property.

The distributive property says:

But in this case, the 8 only multiplies the 6, and not the 2. The correct procedure is:

The correct answer is 64

Given:

A cylinder is given with 5.64 cm deep and 5.25 cm diameter.

Required:

Total volume of 4 cylinders.

Explanation:

Diameter of cylinder d = 5.25 cm

Height of cylinder or deepness of cylinder h = 5.64 cm

Radius r of cylinder is

volume of cylinder is

here we need volume of 4 cylinder

for this we just multiply v with 4

Final Answer:

The volume of 4 cylinder is 488.121 cube cm

Given:

The population of a town increases by 9 % annually.

The current population is 4,500.

Required:

We need to find the equation that gives the population of the town.

Explanation:

The population can be found by the following equation.

Let now be the current population of the town =4500.

Let Next be the population of the town.

The population can be found by the following equation.

Take the common term now out.

Final answer:

approximatesThe equation of a line is given by

Taking two points from the line of best fit

Point A(14,200) and Point B (18,400)

Hence, the equation that best approximate the trend line is y=50x-500

Answer:

Explanation:

The equivalent equation of 6x + 9 = 12  is 2x + 3  = 4.

Another equivalent equation of 6x + 9 = 12 is 3x + 4.5 = 6

Equivalent equations are algebraic equations that have identical solutions or roots. In other words,  equivalent equations are equations that have the same answer or solution.

Therefore, the equivalent equation of 6x + 9 = 12 can be calculated as follows:

6x + 9 = 12

Divide through by 3

6x / 3 + 9 / 3 = 12 / 3

2x + 3  = 4

Therefore, the equivalent equation of 6x + 9 = 12 is 2x + 3  = 4

Another equation that is equivalent to 6x + 9 = 12 is 3x + 4.5 = 6

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f(x) = -16x^2 + 36

Where:

f(x) = height of the object

x = seconds after being dropped.

f(-1) = -16 (-1)^2 + 36

f(-1) = -16 (1) + 36

f(-1) = 20

-1 seconds after the object was dropped, the object was 20 ft above the ground.

This interpretation does not make sense, because seconds can't be negative.

f(0.5) = -16 (0.5)^2 + 36

f(0.5) = -16 (0.25) +36

f(0.5) = -4 + 36

f(0.5) = 32

0.5 seconds after the object was dropped, the object was 32 ft above the ground.

This interpretation makes sense in the context of the problem.

f(2) = -16 (2)^2 + 36

f(2) = -16 (4) +36

f(2) = -64+36

f(2) = -28

2 seconds after the object was dropped, the object was -28 ft above the ground.

This interpretation does not make sense in the context of the problem, because the height can't be negative.

Based on the observation, the domain of the function is real numbers in a <- x <-b , possible values of x where f(x) is true.

before the object is released x=0

next, calculate x when f(x)=0 ( after the object hits the ground)

0= -16x^2+36

16x^2 = 36

x^2 = 36/16

x^2 = 2.25

x = √2.25

x = 1.5

0 ≤ x ≤ 1.5

..Given an isosceles trapezoid

The following are the properties of an isosceles trapezoid

The legs are congruent by definition (From the diagram, the legs are JM and KL)

The lower base angles are congruent. The lower base angles are

The upper base angles are congruent. The upper base angles are

Any lower base angle is supplementary to any upper base angle. This means that

Also,

Hence

m∠J = 61⁰

m∠L = 119⁰

m∠M = 119⁰

Factorize both quadratic polynomials, as shown below

Similarly,

Thus,

Therefore, since the denominator cannot be equal to zero.

Then, provided that a is different than -1,

We will have the following:

Answer:

y = x + 1/10

Step-by-step explanation:

Rewrite the following equation in slope-intercept form: 10x − 10y = –1 ?

slope intercept form: y = mx + b so you are solving for y:

10x − 10y = –1

subtract 10x from both sides:

10x − 10y – 10x = –1 – 10x

-10y = –1 – 10x

divide all terms by -10:

-10y/(-10) = –1/(-10) – 10x/(-10)

y = 1/10 + x

rearrange for slope intercept form: y = mx + b

y = x + 1/10

Answer:

[tex]y=x+\dfrac{1}{10}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Given equation:

[tex]10x-10y=-1[/tex]

To write the given equation in slope-intercept form, perform algebraic operations to isolate y.

Add 10y to both sides of the equation:

[tex]\implies 10x-10y+10y=10y-1[/tex]

[tex]\implies 10x=10y-1[/tex]

Add 1 to both sides of the equation:

[tex]\implies 10x+1=10y-1+1[/tex]

[tex]\implies 10x+1=10y[/tex]

[tex]\implies 10y=10x+1[/tex]

Divide both sides of the equation by 10:

[tex]\implies \dfrac{10y}{10}=\dfrac{10x+1}{10}[/tex]

[tex]\implies \dfrac{10y}{10}=\dfrac{10x}{10}+\dfrac{1}{10}[/tex]

[tex]\implies y=x+\dfrac{1}{10}[/tex]

Therefore, the given equation in slope-intercept form is:

[tex]\boxed{y=x+\dfrac{1}{10}}[/tex]

Simple interest = PRT/100

where p = $3600

R=8

T=10

Substituting into the formula;

S.I = $3600 x 8 x 10 /100

=$36 x 8 x 10

=$2880

Answer:

Step-by-step explanation

Correct option is A)

C.I. for the third year = Rs. 1,452.

C.I. for the second year = Rs. 1,320

∴ S.I on Rs. 1,320 for one year = Rs. 1,452− Rs. 1,320= Rs. 132.

Rate of interest =

1,320

132×100

​

=10%.

Let the original money be Rs. P.

Amount after 2 year − amount after one year =C.I. for second year.

P(1+

100

10

​

)

2

−P(1+

100

10

​

)=1,320

P[(

100

110

​

)

2

−

100

110

​

]=1,320

⇒P[(

10

11

​

)

2

−

10

11

​

]=1,320⇒P(

100

121

​

−

10

11

​

)= Rs. 1,320

⇒P×

100

11

​

=Rs.1,320⇒P=

11

1,320×100

​

= Rs. 12,000

∴ Rate of interest =10%

and Original sum of money = Rs. 12,000

First we have to find the missing angle on each case.

In the first triangle we have

180°-(28°+80°)=72°

In the second triangle we have

180°-(28°+71°)=81°

Since the values of the angles are not the same for both triangles they are not similar.

The torque at the end is equal to 45 Nm.

Torque can be defined as a measure of the amount of force which causes a physical object to rotate about an axis. This ultimately implies that, torque is a force which tends to cause the rotation of a physical object about an axis.

Mathematically, torque can be calculated by using this formula:

τ = Fd

Where:

In this scenario, we can reasonably infer and logically deduce that the torque at the end would be equal to 45 Newton meter (Nm) because the force was not applied over a perpendicular distance.

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Step 1

Properties of a Rhombus

Below are some important facts about the rhombus angles:

Rhombus has four interior angles.

The sum of interior angles of a rhombus add up to 360 degrees.

The opposite angles of a rhombus are equal to each other.

The adjacent angles are supplementary.

In a rhombus, diagonals bisect each other at right angles.

The diagonals of a rhombus bisect these angles.

Step 2

From the figure

Angle DGF = Angle DEF = 118

Step 3

Since adjacent angles are supplementary, that is add to 180 degrees

Step 4

The diagonals of a rhombus bisect these angles

Step 5

The opposite angles of a rhombus are equal to each other.

Final answer